Decreasing rate of growth method is applied for cities nearing its saturated population which shows decrease in population growth.
In This Article
Decreased Rate of Growth Method
The rate of population growth never remains constant for a city throughout its span of development.
The population growth shows increase in growth rate till it reaches the saturation point. Saturation point is established with the limitations in on economic opportunities in the city.
When the city is newly developed, it shows slow increase in growth rate. After a while, the increase in growth rate is rapid. Again, as the population moves towards the saturation, increase in growth rate is decreased.
Disadvantages of Decreased Growth Rate Method:
- Population at each and every successive decade is to be calculated. (No formula exists to directly calculate population at the required decade)
Decreasing Rate of Growth Method Steps
- Calculate percent increase in population of the decades.
- Calculate percent decrease in this percent increase in population.
- Find out average percent decrease in population.
- Estimate the population of the present decade by subtracting the average percent decrease from the last percent increase in population.
Where Decreasing Rate of Growth Method is Used?
For the city/town which is approaching its saturation population, decreased rate of growth method can be applied.
Additionally, this method only applies if a decrease in increase of growth rate of population is observed.
Decreasing Rate of Growth Method Formula
![P_{n}=P(n-1)+[\frac{r(n-1)-S}{100}]*P_{(n-1)}](https://s0.wp.com/latex.php?latex=P_%7Bn%7D%3DP%28n-1%29%2B%5B%5Cfrac%7Br%28n-1%29-S%7D%7B100%7D%5D%2AP_%7B%28n-1%29%7D&bg=ffffff&fg=000&s=0&c=20201002)
Where,
Pn = Population at nth (required) decade
P(n-1) = Population of last known decade (which is just preceding to required decade
r(n-1) = Growth rate of previous decade
S = average decrease in growth rate
Decreasing Rate of Growth Method Example
| Year | 1971 | 1981 | 1991 | 2001 | 2011 |
| Population | 40,65,698 | 62,20,406 | 94,20,644 | 1,38,50,507 |
Step1: Given Data:
Pn = Population at nth (required) decade
P(n-1) = Population of last known decade (which is just preceding to required decade
r(n-1) = Growth rate of previous decade
S = average decrease in growth rate
Step2: Find percent decrease in increase in population per decade
(% increase in population is calculated in similar manner as % increase in geometrical increase method)
| Year | Population | Increase per Decade | % Increase per Decade | % Decrease in % Increase of Growth Rate |
| 1971 | 40,65,698 | – | – | |
| 1981 | 62,20,406 | 21,54,708 | 21/40 * 100 = 53% | – |
| 1991 | 94,20,644 | 32,00,238 | 51.45% | 1.55 % |
| 2001 | 1,38,50,507 | 44,29,863 | 47.02% | 4.43 % |
| 2011 | 1,67,87,941 | 29,37,434 | 21.21% | 25.81 % |
Step3: Find average % increase per decade
= 53 + 51.45 + 47.02/3
= 50.49 %
Step4: Find net increase in population
Modify the % increase in population by considering the % decrease obtained as follows:
| Year | % increase of last decade | Avg % decrease | Net % increase |
| 2011 | 47.02 % | 2.99 % | 44.03 % |
Step5: Find the population at 2011
= 1,38,50,507 + 44.03 % of 1,38,50,507
= 1,38,50,507 + 60,98,378
= 1,99,48,885
Summary
With the limitations on economic opportunities, post the saturation point of development of the city, a decrease in the growth rate of its population is observed. Under such circumstances, decreasing growth rate method of population forecast can be adopted.
![\mathbf{P_{n}=P(n-1)+[\frac{r(n-1)-S}{100}]*P_{(n-1)}}](https://s0.wp.com/latex.php?latex=%5Cmathbf%7BP_%7Bn%7D%3DP%28n-1%29%2B%5B%5Cfrac%7Br%28n-1%29-S%7D%7B100%7D%5D%2AP_%7B%28n-1%29%7D%7D&bg=ffffff&fg=000&s=0&c=20201002)
Population at the end of every successive decade is to be calculated in decreasing growth rate method of population forecast.
FAQ
Which method is suitable if the growth rate is decreasing?
Decreasing rate of growth method